Pressure-induced high-spin/low-spin disproportionated state in the Mott insulator FeBO3

The pressure-induced Mott insulator-to-metal transitions are often accompanied by a collapse of magnetic interactions associated with delocalization of 3d electrons and high-spin to low-spin (HS-LS) state transition. Here, we address a long-standing controversy regarding the high-pressure behavior of an archetypal Mott insulator FeBO3 and show the insufficiency of a standard theoretical approach assuming a conventional HS-LS transition for the description of the electronic properties of the Mott insulators at high pressures. Using high-resolution x-ray diffraction measurements supplemented by Mössbauer spectroscopy up to pressures ~ 150 GPa, we document an unusual electronic state characterized by a “mixed” HS/LS state with a stable abundance ratio realized in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R\overline{3 }c$$\end{document}R3¯c crystal structure with a single Fe site within a wide pressure range of ~ 50–106 GPa. Our results imply an unconventional cooperative (and probably dynamical) nature of the ordering of the HS/LS Fe sites randomly distributed over the lattice, resulting in frustration of magnetic moments.

pressure. The spectra at higher pressures, 115 and 140 GPa, were collected using energy-domain synchrotron Mössbauer spectroscopy (SMS) carried out at the beamline ID18 at ESRF at temperatures down to 3 K (see [5] for more details). These spectra were collected with the source at RT and, therefore, are affected by the 2 nd order Doppler shift. Diffraction images were collected using MAR345 image plates. The image data were integrated using the FIT2D and DIOPTAS programs 6,7,8 and the resulting diffraction patterns were analyzed by Rietveld refinement using GSAS 9 and EXPGUI 10 software.
Isobaric powder XRD low-temperature measurements were carried out at the ID09A beamline of ESRF (Grenoble) with a wavelength of  = 0.415244 Å using MAR555 flat panel image plate and a He cryostat with cooling down to 10 K. He was used as a pressure medium and Pt as an in-situ XRD pressure marker. Pressure values were calculated taking into account Pt thermal expansion. 11

Sample preparation
Transparent light-green single plate-shaped crystals of FeBO3 (the plane of the plate parallel the basal (111) plane) with an average size of 0.03 x 0.02 x 0.01 mm 3 were pre-selected on a threecircle Bruker diffractometer equipped with a SMART APEX CCD detector and a high-brilliance Rigaku rotating anode (Rotor Flex FR-D, Mo-Kα radiation) with Osmic focusing X-ray optics.

Data collection
The single-crystal XRD experiments were conducted in four runs.
Run#1 was carried out at the 13-IDD beamline at the Advanced Photon Source (APS), Chicago, USA (MAR165 CCD detector,  = 0.3344 Å, beam size 2(V) x 4(H) μm 2 ). Sample-to-detector distance, coordinates of the beam center, tilt angle and tilt plane rotation angle of the detector images were calibrated using LaB6 powder. XRD wide images were collected during continuous rotation of DACs typically from -35 to +35 on omega; while XRD single-crystal data collection experiments were performed by narrow 0.5° scanning of the same omega range. DIOPTAS software 7 was used for preliminary analysis of the 2D images and calculation of pressure values from the positions of the XRD lines of Ne.
A single crystal of FeBO3 with an average size of 0.03 x 0.02 x 0.01 3 mm together with a small ruby chip (for pressure estimation) were loaded into BX90-type DAC equipped with Boehler-Almax diamonds with 250 μm culet size. A hole with diameter about 120 μm in rhenium gasket pre-indented to 30 μm was served as a pressure chamber. Neon was used both as a pressure transmitting medium and as a pressure standard. Neon was loaded with a gas loading system installed at the Bayerisches Geoinstitut. 12 The pressure was increased manually by tightening the screws. The DAC was compressed to 62.5(5) GPa with step 2-11 GPa with wide images being collected at each pressure point. The single-crystal XRD datasets have been collected only at 5 selected pressure points (namely at ambient pressure, 11.5(1), 45.8(3), 55.7(5) and 61.0(5) GPa) in order to determine orientation matrix of the single-crystal and refine the matrix after the phase transition. The indexing of the unit cell was performed using CrysAlisPro software 13 . Intensities of the diffraction reflections were extracted from the wide images by means of GSE_ADA/RSV package according to procedure described by P. Dera et al. 14 Run#2 and #3 were carried out at the ID15B beamline at the European Synchrotron Radiation Facility (ESRF), Grenoble, France (MAR555 flat panel detector,  = 0.41114 Å, beam size 10(V)x10(H) μm 2 ). Sample-to-detector distance, coordinates of the beam center, tilt angle and tilt plane rotation angle of the detector images were calibrated using Si powder. XRD wide images were collected during continuous rotation of DACs from -20 to +20 on omega; while data collection experiments were performed by narrow 0.5° scanning from -30 to +30 on omega. In Run#2 the single-crystal of FeBO3 was loaded in a membrane-driven DAC, with 300 µm Boehler-Almax diamond anvils. A hole with diameter about 150 μm in a steel gasket pre-indented to 35 μm was used as a pressure chamber. In Run#3 the single-crystal of FeBO3 was loaded in BX90type DAC, with 250 µm Boehler-Almax diamond anvils. A hole with diameter about 120 μm in rhenium gasket pre-indented to 30 μm was used as a pressure chamber. Neon was used both as a pressure transmitting medium and as a pressure standard.
Processing of XRD data (the unit cell determination and integration of the reflection intensities) were performed using CrysAlisPro software 13 . Empirical absorption correction was applied using spherical harmonics, implemented in the SCALE3 ABSPACK scaling algorithm, which is with a wavelength of 0.2898 Å with x-ray beam focused to 3(V) x 8(H) μm 2 (e.g. fullwidth at half maximum). Compression was conducted using the symmetric cells. Data was collected using Perkin Elmer XRD1621 flat panel detector. Preliminary calibration was done with CeO2 and further refined using CrysAlisPro software employing a piece of the orthoenstatite coming from the same batch as in Run#3. Similar is the situation with absorption correction.
For measurements at P02.2, for the study exceeding 1 Mbar we used crystal smaller than 0.020 x 0.020 x 0.005 mm 3 . We used beveled Boehler-Almax diamonds of 150/300 μm culet size. In contrast to the other runs, in order to boost the signal to noise ratio we used an amorphous metal insert (with an initial hole of 75 μm) into a Re gasket. Such geometry of a sample chamber produces lower scattering even if the gasket is hit by the tails of a larger x-ray beam. Prior to compression, Ne was loaded as pressure medium.
The following sequence was recorded during the spin state transition.
Fig. S1. 2D diffraction patterns (collected with DAC oscillation of ±20º) indicating diffraction response from FeBO3 with a focus given to a specific diffraction spot changing as a function of pressure. HS and LS contributions are present at lower 2θ and higher 2θ, respectively. Center of the diffraction pattern is in the direction of the top left corner of the diffractogram. At ~50 GPa we observed a negligible contribution from LS HP state. At ~51.2(1) GPa the abundance from the low spin state has increased. HS LP almost disappeared at ~54.2(1) GPa as most of the intensity is transferred into the LS state. Certain diamond and Ne diffraction lines are indicated.

Structure solution and refinement of FeBO3
At ambient pressure FeBO3 adopts crystal structure of calcite (CaCO3, sp.gr. 3 ̅ c, Z = 6) and all atoms are located on special positions: Fe atom occupies Wycoff position 6b (0, 0, 0), B -6a (0, 0, 0.25) and oxygen is located on 18e (x, 0, 0.25). Therefore, only one oxygen coordinate, thermal parameters and scale factor have to be refined. Since body of the diamond anvil cell shadows more than 50% of the diffraction reflections, the reflection datasets are incomplete. In order to improve data/parameter ratio, we refined atomic thermal parameters in isotropic approximation. The structures were refined by full-matrix least squares against F 2 using the SHELXL-2014/7 15 (at certain points using OLEX2 16 frontend) and JANA2006 17 software.
The detailed summary of the crystal structure refinements along with information on unit cell parameters, atomic coordinates and isotropic displacement parameters are summarized in Tables 1, 2 and 3. Polyhedral volumes were determined with VESTA software 18 . Our SC-XRD data can be considered as a new reference for the FeBO3 phase diagram and for the V(P) data.

SC versus PWD XRD data
Comparison of our SC and PWD data, and PWD data published in literature (e.g. 19 ) indicate an appreciable difference in their V(P) behavior. This discrepancy may be related to differences in the initial state of sample material on the microscale. Following the recent discussion 20 , considering PWD case one may expect additional strains or stresses due to grain-grain interactions.
Particularly, some strongly correlated systems demonstrating spin state transitions are exceptionally sensitive to the effects of deviatoric stress and strain effects on the grain-grain interactions occurring in sample chambers of DACs. 20 These effects may induce a distortion of the structure, adjustment of local crystal field at Fe 3+ sites, presumably affecting the onset of spin crossover. In addition, the grinding process, which is essential for powder preparation, should significantly increase the defect concentration in the grains and, thus, induce additional microstrain fields in the vicinity of Fe ions. In contrast, in a SC study one minimizes the contribution from undesirable effects of grain boundaries, intergrain stresses, and grinding-induced defects, and thus transform the materials to a configuration closer to thermodynamic equilibrium 20 (for a more detailed discussion of this problem see also 21 ).
We note that in the HS LP phase the increasing deviation of the PWD V(P) data from SC EOS show that the volume difference ΔV remains stable (see Fig. S5) suggesting that the contribution from undesirable stresses and strains does not change appreciably with pressure increase up to ~110 GPa. However, at ~110 GPa one observes a drastic increase of discrepancy of the SC and PWD data: while SC shows the sharp transition to the C2/c structure, PWD data demonstrate a very sluggish structural transformation, whose onset is indicated by a sharp increase of the ΔV value above 110 GPa (Fig. S5). Such a change of the V(P) behavior suggests an onset of a structural transformation related to a significantly increased strain resulting in growing discrepancies with a hydrostatic reference, e.g. SC data.  Representation units correspond to Å. Upon loading into sample chamber, the orientation of the crystal was such that the c axis of 3 ̅ c was directed along compression axis as indicated by x-ray beam direction. After the transformation to C2/c, a axis of C2/c was directed perpendicular to c of 3 ̅ c and c axis of C2/c was oriented in the direction very similar to a axis of 3 ̅ c. Picture was prepared using python3 and plotly library using information of crystal orientation determined with CrysAlisPro. 13 The code is derived from the open source K. Glazyrin's github repository located at https://github.com/lorcat/Crysalis-CIFOD.    4.62920(10) 4.5242 (2) 4.4581 (7) 4.3275 (6) c (Å) 14.4849 (7) 13.694 (11) (2) c (Å) 14.058 (7) 13.550 (6) 13.144 (6) 12.559 (14) 7.3926 (5) b (Å) 4.1253 (4) c (Å) 4